Year: 2025
Type: article
Abstract: We consider a periodic quantum graph in the form of a rectangular lattice with the δ-coupling of strength γ in the vertices perturbed by changing the latter at an infinite straight array of vertices to a γ ~ ≠ γ . We analyze the band spectrum of the system and show that it remains preserved as a set provided γ ~ > γ > 0 while for all the other combinations additional band appear in some or all gaps of the unperturbed system. We also prove that for a randomly chosen positive energy, the probability of existence of a state exponentially localized in the vicinity of the perturbation equals 1 2 .
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408894592